STATISTICAL TREATMENTS 205 



(100 per cent — 68 per cent) of the samples of the untreated population 

 will deviate from the mean this much. 



Normal Deviate: In the previous few paragraphs we have been speak- 

 ing, without defining it, about a statistic known as the normal deviate. A 



Fig. 15-2. The normal curve, showing the relationship between the stand- 

 ard deviation and the included area under the curve. 



value can be tested for significant deviation from the population mean by 

 expressing the deviation from the mean in terms of standard deviations. 

 The normal deviate (c) is 



(x — m) 



C =z 



(T 



which indicates that the value differs from the mean by a certain num- 

 ber of standard deviations. Published tables of probability tell us how 

 frequently such deviates occur in the normal curve. In 5 per cent of the 

 samples, c is 1.96 or greater; in 1 per cent of the samples, c is 2.58 or 

 greater; and in 0.1 per cent of the samples, c is 3.29 or greater. 



The normal deviate is also used to test the significance of the differ- 

 ence between the mean of a sample and the mean of a population. In 

 this case, the standard error of the mean is used instead of the population 

 standard deviation: 



X — m X — m 



c = = = 



o"5 a-/Vw 



